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Low Temperature Physics

Stochastic-parametric amplification of narrow-band signals in a single-junction SQUID interferometer

Oleg G. Turutanov, V. I. Shnyrkov, A. M. Glukhov

Published Jan 1, 2008• 1 citation
Publisher

Abstract

The features of the response of a single-junction superconducting quantum interferometer to a low-frequency harmonic signal in the presence of noise and a high-frequency electromagnetic field are investigated through numerical solution of the equations of motion. It is shown that in this situation a system described by a double-well potential will display stochastic-parametric amplification of weak harmonic signals owing to the cooperative effects of noise and the high-frequency field. The gain is a nonmonotonic function of the amplitude of the high-frequency field and the variance of the noise flux and passes through a maximum. A detailed numerical analysis of the dependence of the gain on the noise intensity and on the frequency and amplitude of the high-frequency field is carried out in the stochastic, parametric, and stochastic-parametric amplification regimes. It is shown that at optimal amplitude of the high-frequency field the gain for a weak harmonic signal reaches rather high values (10–30). The specific properties of stochastic-parametric amplification are discussed, and the possible applications of this effect for constructing input circuits of detectors based on SQUIDs with registration of weak narrow-band information signals are considered.

DOI
10.1063/1.2832354

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•Jan 1, 2015•4 citations
The features of the response of a single-junction superconducting quantum interferometer to a low-frequency harmonic signal in the presence of noise and a high-frequency electromagnetic field are investigated through numerical solution of the equations of motion. It is shown that in this situation a system described by a double-well potential will display stochastic-parametric amplification of weak harmonic signals owing to the cooperative effects of noise and the high-frequency field. The gain is a nonmonotonic function of the amplitude of the high-frequency field and the variance of the noise flux and passes through a maximum. A detailed numerical analysis of the dependence of the gain on the noise intensity and on the frequency and amplitude of the high-frequency field is carried out in the stochastic, parametric, and stochastic-parametric amplification regimes. It is shown that at optimal amplitude of the high-frequency field the gain for a weak harmonic signal reaches rather high values (10–30). The specific properties of stochastic-parametric amplification are discussed, and the possible applications of this effect for constructing input circuits of detectors based on SQUIDs with registration of weak narrow-band information signals are considered.
In a single-junction niobium superconducting quantum interferometer (RF SQUID loop), a weak low-frequency harmonic signal is amplified when quasi-white Gaussian noise magnetic flux is applied to the loop; such amplification is due to stochastic resonance (SR). We have experimentally shown that if the suboptimal flux noise intensity is insufficient for SR, the mean rate of transitions between the metastable states of the loop, and thus the signal gain, can be controlled by an additional deterministic alternating magnetic flux with frequency being much higher than that of the useful signal to provide the maximal possible gain. The frequency characteristics of a multi-tone composite signal amplification in the cases of controlled stochastic amplification and “pure” SR are compared to each other.
There is currently fundamental and technological interest in measuring and manipulating nanoscale magnets, particularly in the quantum coherent regime. To observe the dynamics of such systems one requires a magnetometer with not only exceptional sensitivity but also high gain, wide bandwidth, and low backaction. We demonstrate a dispersive magnetometer consisting of a two-junction superconducting quantum interference device (SQUID) in parallel with an integrated, lumped-element capacitor. Input flux signals are encoded as a phase modulation of the microwave drive tone applied to the magnetometer, resulting in a single quadrature voltage signal. For strong drive power, the nonlinearity of the resonator results in quantum limited, phase sensitive parametric amplification of this signal, which improves flux sensitivity at the expense of bandwidth. Depending on the drive parameters, the device performance ranges from an effective flux noise of 0.29 $\ensuremath{\mu}{\ensuremath{\Phi}}_{0}$Hz${}^{\ensuremath{-}1/2}$ and 20 MHz of signal bandwidth to a noise of 0.14 $\ensuremath{\mu}{\ensuremath{\Phi}}_{0}$Hz${}^{\ensuremath{-}1/2}$ and a bandwidth of 0.6 MHz. These results are in excellent agreement with our theoretical model.
We report the lowest noise temperature of any microwave amplifier except the maser. This amplifier is a nearly degenerate superconducting parametric amplifier at X-band consisting of a low β, thin film, single junction SQUID, a monolithic 50 Ω to 1 Ω impedance matching network, and a cooled circulator. Nb/Nb2O5/Pb alloy junctions were incorporated into Nb and Pb-in circuitry on 1×2 cm silicon chips. The SQUID was phase-biased near 90° and driven by an external pump at approximately twice the operating frequency. The self-resonance frequency of the SQUID inductance and junction capacitance was set at the operating frequency of 8.2GHz. The operating charac teristics depended on the pump amplitude, the junction phase bias, and the SQUID parameters. For small values of\beta < 1, the maximum gain in both the signal and idler channels was ≈10dB, the bandwidth = 170MHz, and the single-sidehand noise temperature was 6K with an uncertainty of (+15 to -7)K. For higher β, the gain increased to nearly 30dB with increased noise and parametric oscillations occurring near the pump subharmonic frequency.
In this thesis I present different experiments on superconducting circuits exploring parametric interactions with external signals and the vacuum in the microwave regime. These parametric processes are the result of the periodic modulation of a property of a system which results in different interactions. The systems used in this thesis are circuits where the nonlinear inductance of a superconducting quantum interference device (SQUID) is parametrically driven.I present the first experimental observation of the dynamical Casimir effect (DCE), since it was predicted in 1970. The DCE is an interaction between the vacuum and a periodically modulated boundary condition of the electromagnetic field, here implemented by a flux-tuned SQUID. In essence the modulated boundary will parametrically amplify the vacuum fluctuations which results in the pairwise generation of photons over a broad frequency range. I have characterized the system and measured the statistical properties of the emitted radiation to show that the radiation exhibits two-mode squeezing.Next, I present measurements on a superconducting multimode resonator containing a SQUID. I show that it is possible to get parametric amplification by driving the SQUID at either twice the frequency of one of the modes or by driving it at the sum of two mode frequencies. In both cases I show that it is possible to reach quantum-limited noise performance.In the same system I also demonstrate frequency conversion which occurs when the system is pumped at the difference frequency between two modes. Microwave photons are coherently transferred from one mode to the other. I show that the coupling strength depends linearly on the applied pump amplitude.The thesis also contains a linearized theoretical model to describe and analyze the flux-pumped SQUID. The model describes an equivalent circuit element called the pumpistor, with an impedance which depends on the pump phase. I show that under specific conditions the impedance becomes real and negative allowing pump power to be injected into the circuit, providing gain.Finally I also present a demonstration of an on-chip Mach-Zehnder interferometer. This experiment uses the tunability of the SQUID to provide a controllable phase shift in one of the interferometer arms. The transmission through the device can be modulated with a maximum change of 45 dB.